Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Finsler Geometry, Sapporo 2005 — In Memory of Makoto Matsumoto, S. V. Sabau and H. Shimada, eds. (Tokyo: Mathematical Society of Japan, 2007), 343 - 373
The Chern-Finsler connection and Finsler-Kähler manifolds
In this paper, we shall discuss the theory of connection in complex Finsler geometry, i.e., the Chern-Finsler connection $\nabla$ and its applications. In particular, we shall investigate (1) the ampleness of holomorphic vector bundles over a compact complex manifold which is based on the study due to [Ko1], (2) some special class of complex Finsler metrics and its characterization in terms of torsion and curvature of $\nabla$, and in the last section, (3) the characterization of Finsler-Kähler manifolds in terms of the Cartan connection $D$ which is naturally induced on the real tangent bundle from $\nabla$.
Received: 27 May 2006
Revised: 13 June 2006
First available in Project Euclid: 16 December 2018
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Aikou, Tadashi. The Chern-Finsler connection and Finsler-Kähler manifolds. Finsler Geometry, Sapporo 2005 — In Memory of Makoto Matsumoto, 343--373, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04810343. https://projecteuclid.org/euclid.aspm/1545001111